Importance sampling for partially observed temporal epidemic models

Abstract

We present an importance sampling algorithm that can produce realisations of Markovian epidemic models that exactly match observations, taken to be the number of a single event type over a period of time. The importance sampling can be used to construct an efficient particle filter that targets the states of a system and hence estimate the likelihood to perform Bayesian inference. When used in a particle marginal Metropolis Hastings scheme, the importance sampling provides a large speed-up in terms of the effective sample size per unit of computational time, compared to simple bootstrap sampling. The algorithm is general, with minimal restrictions, and we show how it can be applied to any continuous-time Markov chain where we wish to exactly match the number of a single event type over a period of time.

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Notes

  1. 1.

    Also known as the Gillespie algorithm or the Doob-Gillespie algorithm.

  2. 2.

    In fact this can be done analytically for this model.

  3. 3.

    This condition may not be true after the final observed infection event, depending on what other observations are made on the system afterwards.

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Acknowledgements

This research was supported by an ARC DECRA fellowship (DE160100690). AJB also acknowledges support from both the ARC Centre of Excellence for Mathematical and Statistical Frontiers (CoE ACEMS), and the Australian Government NHMRC Centre for Research Excellence in Policy Relevant Infectious diseases Simulation and Mathematical Modelling (CRE PRISM\(^2\)). Supercomputing resources were provided by the Phoenix HPC service at the University of Adelaide. AJB would also like to thank Joshua Ross and James Walker for comments on an earlier draft of the manuscript.

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Black, A.J. Importance sampling for partially observed temporal epidemic models. Stat Comput 29, 617–630 (2019). https://doi.org/10.1007/s11222-018-9827-1

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Keywords

  • Importance sampling
  • Markov chain
  • Epidemic modelling
  • Particle filter